Question

How do I add a whole number with a fraction?

Answer 1

Hint:
Start with assuming a whole number as ‘m’ and a fraction as $\dfrac{a}{b}$ . A whole number can be expressed as a fraction by writing $1$ in the denominator. This makes the assumed whole number as $\dfrac{m}{1}$ . For adding two fractions, multiply both the denominators and cross multiply in numerators, i.e. $\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{{a \times d + c \times b}}{{b \times d}}$ . Substituting this expression, we can get the required solution.

Complete step by step solution:
Here in this question, we need to describe the method of addition of a whole number and a fractional number.
Before starting with the solution, we must understand a few terms related to the above problem. The whole numbers are defined as the positive integers including zero. The whole number does not contain any decimal or fractional part. It means that it represents the entire thing without pieces. A fraction has two parts, namely numerator, and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
For the addition of fractions, if the denominator is the same for both the fractions, then they follow:
\[ \Rightarrow \dfrac{a}{b} + \dfrac{c}{b} = \dfrac{{a + c}}{b}\]
If the denominators of two fractions are not the same, then the addition can be done as:
$ \Rightarrow \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{{ad + cb}}{{bd}}$
As we know that any whole number, is also a rational number, and can be represented in a fractional form by putting $1$ in the denominator, i.e.
Assuming that a whole number is ‘m’ and a fraction as $\dfrac{a}{b}$
$ \Rightarrow m + \dfrac{a}{b} = \dfrac{m}{1} + \dfrac{a}{b}$
Now this can be solved by taking the case where the denominator of two fractions is not the same
Therefore, we can multiply the denominators:
$ \Rightarrow \dfrac{m}{1} + \dfrac{a}{b} = \dfrac{{\left( {m \times b} \right) + \left( {1 \times a} \right)}}{{1 \times b}}$
We can further simplify the numerator to get:
$ \Rightarrow \dfrac{{\left( {m \times b} \right) + \left( {1 \times a} \right)}}{{1 \times b}} = \dfrac{{mb + a}}{b}$
Thus, we showed the procedure of the addition of a whole number and a fraction. The whole number ‘m’ and fraction $\dfrac{a}{b}$ will give the addition as $\dfrac{{mb + a}}{b}$ .

Note:
In the above solution, we got a general expression for any whole number and fraction. We can check our solution by taking an example with the whole number $3$ and the fraction $\dfrac{5}{6}$ . So now we can put $m = 3$ and $\dfrac{a}{b} = \dfrac{5}{6}$ in expression $\dfrac{{mb + a}}{b}$ to get the addition. Therefore, $m + \dfrac{a}{b} = \dfrac{{mb + a}}{b} \Rightarrow 3 + \dfrac{5}{6} = \dfrac{{3 \times 6 + 5}}{6} = \dfrac{{23}}{6}$.